Mean quadratic convergence of signed random measures
Jacob, Pierre ; Oliveira, Paulo Eduardo
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 119-123 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper.

Publié le : 1991-01-01
Classification:  28A20,  28C05,  60B10,  60F25,  60G57 
@article{116948,
     author = {Pierre Jacob and Paulo Eduardo Oliveira},
     title = {Mean quadratic convergence of signed random measures},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {119-123},
     zbl = {0731.60030},
     mrnumber = {1118295},
     language = {en},
     url = {http://dml.mathdoc.fr/item/116948}
}

Jacob, Pierre; Oliveira, Paulo Eduardo. Mean quadratic convergence of signed random measures. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 119-123. http://gdmltest.u-ga.fr/item/116948/

Billingsley P. Convergence of Probability Measures, John Wiley & Sons, 1968. | MR 0233396 | Zbl 0944.60003

Bonkian S.M. Contribution à l'étude des mesures aléatoires du second ordre, Thèse du 3$^{ {ème}}$ cycle, Université des Sciences et Techniques de Lille I, 1983.

Halmos P.R. Measure Theory, D. Van Nostrand Co. Inc., Princeton, New Jersey, 1950. | MR 0033869 | Zbl 0283.28001

Jacob P. Convergence uniforme à distance finie de mesures signées, Ann. Inst. Henri Poincaré, 15 (1979), n$^{ o}$4, 355-373. (1979) | MR 0567733 | Zbl 0439.60006

Kallenberg O. Random Measures, Academic Press, 1976. | MR 0431373 | Zbl 0694.60030

Lima E.L. Espaços métricos, Projecto Euclides, IMPA, Rio de Janeiro, 1983. | Zbl 0529.54001

Marle C.-M. Mesures et Probabilités, Enseignement des Sciences, Hermann, Paris, 1974. | MR 0486378 | Zbl 0306.28001

Oliveira P.E. Convergence de suite de mesures et convergence des masses, Pub. IRMA, Lille, 13 (1988), II. (1988)

Tortrat A. Calcul des probabilités et introduction aux processus aléatoires, Masson, Paris, 1971. | MR 0375403 | Zbl 0212.49201

Varadarajan V.S. Measures on Topological Spaces, Transl. of Ame. Math. Soc., Series 2, 48 (1965), 161-228. (1965)